An air-conditioning device has a duct that emits a flow of conditioned air and at least one circulation circuit intended for fitting out a carriage. The circulation circuit includes an air inlet through which passes an incoming airflow from the duct; at least one conduit for distributing air towards a compartment room, extending between an upstream end and a downstream end, both intended to be laid out in the carriage; a conduit for transferring conditioned air towards another adjacent air circulation circuit, which fits out a carriage adjacent to the first; and means for distributing conditioned air from the air inlet, and distributing the incoming airflow among the distribution and transfer conduits.